### The Cauchy problem and the martingale problem for integro-differential operators with non-smooth kernels

Abels H, Kaßmann M (2009)
Osaka journal of mathematics 46(3): 661-683.

Zeitschriftenaufsatz | Veröffentlicht | Englisch

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Autor*in
Abels, Helmut; Kaßmann, MoritzUniBi
Abstract / Bemerkung
We consider the linear integro-differential operator L defined by Lu(x) = integral(Rn) (u(x + y) - u(x) - 1([1,2])(alpha)1([vertical bar y vertical bar <= 2])(y)y. del u(x))k(x, y)dy. Here the kernel k(x, y) behaves like vertical bar y vertical bar(-n-alpha), alpha is an element of (0, 2), for small y and is Holdercontinuous in the first variable, precise definitions are given below. We study the unique solvability of the Cauchy problem corresponding to L. As an application we obtain well-posedness of the martingale problem for L. Our strategy follows the classical path of Stroock-Varadhan. The assumptions allow for cases that have not been dealt with so far.
Erscheinungsjahr
2009
Zeitschriftentitel
Osaka journal of mathematics
Band
46
Ausgabe
3
Seite(n)
661-683
ISSN
0030-6126
Page URI
https://pub.uni-bielefeld.de/record/1589471

### Zitieren

Abels H, Kaßmann M. The Cauchy problem and the martingale problem for integro-differential operators with non-smooth kernels. Osaka journal of mathematics. 2009;46(3):661-683.
Abels, H., & Kaßmann, M. (2009). The Cauchy problem and the martingale problem for integro-differential operators with non-smooth kernels. Osaka journal of mathematics, 46(3), 661-683.
Abels, H., and Kaßmann, M. (2009). The Cauchy problem and the martingale problem for integro-differential operators with non-smooth kernels. Osaka journal of mathematics 46, 661-683.
Abels, H., & Kaßmann, M., 2009. The Cauchy problem and the martingale problem for integro-differential operators with non-smooth kernels. Osaka journal of mathematics, 46(3), p 661-683.
H. Abels and M. Kaßmann, “The Cauchy problem and the martingale problem for integro-differential operators with non-smooth kernels”, Osaka journal of mathematics, vol. 46, 2009, pp. 661-683.
Abels, H., Kaßmann, M.: The Cauchy problem and the martingale problem for integro-differential operators with non-smooth kernels. Osaka journal of mathematics. 46, 661-683 (2009).
Abels, Helmut, and Kaßmann, Moritz. “The Cauchy problem and the martingale problem for integro-differential operators with non-smooth kernels”. Osaka journal of mathematics 46.3 (2009): 661-683.

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